The average farm size in the United States is 444 acres. A random sample of 40 farms in Oregon indicated a mean size of 430 acres, and the population standard deviation is 52 acres. At a= 0.05, can it be concluded that the average farm in Oregon differs from the national average? Transcription for Educational Website:---**Critical Values:**- **CV1** = - **CV2** = - Selection: invNorm---**Round to Two Decimal Places:**- **CV1** = - **CV2** = ---**f) What formula will we use for the test value?**1. $ t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $2. $ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} $3. Selected: $ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} $4. $ z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} $5. $ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} $---Each formula listed above represents different statistical tests used to calculate test values based on given parameters. Select the appropriate formula depending on your dataset and hypothesis.

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Description: The average farm size in the United States is 444 acres. A random sample of 40 farms in Oregon indicated a mean size of 430 acres, and the population standard deviation is 52 acres. At a= 0.05, can it be concluded that the average farm in Oregon diff

Null hypothesis: H0: μ = 444. Alternative hypothesis: HA : μ ≠ 444 Central Limit Theorem for mean:…

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The average farm size in the United States is 444 acres. A random sample of 40 farms in Oregon indicated a mean size of 430 acres, and the population standard deviation is 52 acres. At a= 0.05, can it be concluded that the average farm in Oregon differs from the national average?

Transcription for Educational Website:

---

**Critical Values:**

- **CV1** =
- **CV2** =

- Selection: invNorm

---

**Round to Two Decimal Places:**

- **CV1** =
- **CV2** =

---

**f) What formula will we use for the test value?**

1. $ t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $

2. $ z = \frac{(\hat{p}_1 - \hat{p}_2) - (p_1 - p_2)}{\sqrt{\hat{p} \cdot \hat{q} \cdot \left( \frac{1}{n_1} + \frac{1}{n_2} \right)}} $

3. Selected: $ z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}} $

4. $ z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}} $

5. $ t = \frac{\bar{x} - \mu}{s / \sqrt{n}} $

---

Each formula listed above represents different statistical tests used to calculate test values based on given parameters. Select the appropriate formula depending on your dataset and hypothesis.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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